CN106357375B - A method of assessment BPSK high specific, which receives, merges error performance - Google Patents

A method of assessment BPSK high specific, which receives, merges error performance Download PDF

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CN106357375B
CN106357375B CN201610720898.9A CN201610720898A CN106357375B CN 106357375 B CN106357375 B CN 106357375B CN 201610720898 A CN201610720898 A CN 201610720898A CN 106357375 B CN106357375 B CN 106357375B
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CN106357375A (en
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李岳衡
孙蔓
潘进勇
徐荣蓉
孙得娣
郭臣
居美艳
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Hohai University HHU
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00Arrangements for detecting or preventing errors in the information received
    • H04L1/20Arrangements for detecting or preventing errors in the information received using signal quality detector
    • H04L1/203Details of error rate determination, e.g. BER, FER or WER
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00Arrangements for detecting or preventing errors in the information received
    • H04L1/20Arrangements for detecting or preventing errors in the information received using signal quality detector
    • H04L1/206Arrangements for detecting or preventing errors in the information received using signal quality detector for modulated signals
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00Modulated-carrier systems
    • H04L27/18Phase-modulated carrier systems, i.e. using phase-shift keying
    • H04L27/22Demodulator circuits; Receiver circuits
    • H04L27/227Demodulator circuits; Receiver circuits using coherent demodulation

Abstract

The method for merging error performance is received the invention discloses a kind of assessment BPSK high specific, consider under AWGN and Rayleigh fading environment, communication system uses BPSK digital modulation and coherent demodulation, receiving end obtains the mutually independent tributary signal of L item, average error rate model when bpsk signal is merged using L branch MRC is established, BPSK high specific is assessed according to average error rate and receives merging error performance;It solves the problems, such as that the computation complexity of the BPSK theory bit error rate under MRC merges is high, can be applied to the bit error rate performance of rapid evaluation mimo system, simplify computation complexity, error rate of system performance can accurately be estimated.

Description

A method of assessment BPSK high specific, which receives, merges error performance
Technical field
The present invention relates to art communication systems field, especially a kind of assessment BPSK high specific, which receives, merges error performance Method.
Background technique
Diversity and combining techniques are received to be acknowledged as resisting one of the most effective means of wireless fading channel in current communication system, It relies primarily on using the redundancy of branch component each during multipath transmisstion the performance for improving system: i.e. first by Receiving end obtains the mutually independent tributary signal of L item, then selects suitable mode to carry out signal according to demand and merges to obtain Diversity gain, enhancing signal quality.Common reception folding have maximum-ratio combing (Maximum Ratio Combining, MRC), equal gain combining (Equal Gain Combinbing, EGC), selection combining (Selection Combinbing, SC) Deng.Existing theory analysis and practice have shown that, MRC is that performance is best in all receptions foldings, in addition its realization technology And it is uncomplicated, so be widely applied in engineering.
In general, the networking that communications carrier can all carry out system performance before formally building mobile communications network is surveyed Examination, performance indexes when being run with assessment system, such as power system capacity, outage probability, the bit error rate etc.;Even if network is built At later, communication equipment is also required to frequent test job performance to feed back and design with evaluation system;Error performance among these is just It is a Xiang Changyong of measurement system performance and important index.But the received BER performance analysis of MRC merging gets up not It is convenient, theoretical miss can be even obtained under binary phase shift keying (Binary Phase Shift Keying, BPSK) modulation The closed form expression of code also can bring certain burden to realization etc. is calculated in line hard ware in view of the complexity of its expression formula, unfavorable In the development trend of green communications.
Summary of the invention
A kind of assessment BPSK high specific is provided the technical problem to be solved by the present invention is to overcome the deficiencies in the prior art The method for merging error performance is received, proposes a kind of consideration additive white Gaussian noise (Additive White Gaussian Noise, AWGN) and Rayleigh Rayleigh fading environment under, communication system use BPSK digital modulation and coherent demodulation when, have L The approximation of branch MRC diversity merging receiver error performance simplifies appraisal procedure.
The present invention uses following technical scheme to solve above-mentioned technical problem:
A kind of assessment BPSK high specific for iing is proposed according to the present invention receives the method for merging error performance, consider AWGN and Under Rayleigh fading environment, communication system uses BPSK digital modulation and coherent demodulation, and it is mutually independent that receiving end obtains L item Tributary signal, when establishing L branch MRC merging, the average error rate model of bpsk signal is assessed according to average error rate BPSK high specific, which receives, merges error performance;Wherein,
Average error rate model are as follows:
Wherein, L is the number of receiving end branch,For the corresponding average received signal-to-noise ratio of each symbol of receiving end.
As a kind of method side of advanced optimizing of assessment BPSK high specific reception merging error performance of the present invention Case, specific step is as follows for the average error rate model:
Step 1: the band logical for setting the branch of receiving end L receives signal as r1(t),r2(t),...,rL(t), different antennae branch The vector form that the bandpass signal that road receives obtains baseband signal after multicarrier orthogonal demodulation matched filtering isIt uses again Different diversity combiners obtains output signal vector to the endWherein, rkIt (t) is kth paths received signal copy, k =1,2 ..., L;
Step 2: finally merging signal output for L input signal of receiving end are as follows:
Wherein, akFor weighting coefficient;
To akIt is normalized:
Step 3: the amplitude of fading α of system transmission symbol meets Rayleigh distribution under Rayleigh fading channel, Its probability density function fα(α) are as follows:
Wherein, e is the nature truth of a matter, and σ is constant and 0,2 σ of σ >2=E [α2] be amplitude of fading α mean-square value, mean valueVariance D [α]=(4- π) σ2/2;The power spectral density of additive white Gaussian noise AWGN is N in channel0;If Transmission end signal emitted energy is Es, every branch receiving end signal instantaneous signal-to-noise ratio is denoted as γk, corresponding to average received Signal-to-noise ratio is denoted asThen have:
According to the instantaneous signal-to-noise ratio γ for every branch receiving end signal that formula (4) obtainskWith the relationship of amplitude of fading α, Go out instantaneous received signal to noise ratio γ according to Jacobian transformation calculations againkProbability density function fγkk) are as follows:
Step 4: when being merged using MRC, akk/Nk, wherein αkIndicate the envelope of kth branch, NkIndicate noise function Rate;If each branch mutually balances, under Rayleigh fading channel, envelope αkRayleigh is obeyed to be distributed, and αk 2Obey card side Distribution and E [αk 2The σ of]=22, then in square of the total envelope in receiving endBe obey freedom degree be 2L chi square distribution and Its probability density function fα(α) are as follows:
Wherein, Γ () is Gamma function, has Γ (L)=(L-1) when L is positive integer!;Each symbol of receiving end Corresponding average received signal-to-noise ratioWith output prompt character signal-to-noise ratioValue be respectively:
Wherein,Subscript MRC indicate maximum-ratio combing, subscript s indicate symbol,Represent MRC merge under the conditions of Instantaneous reception symbol signal-to-noise ratio;According to expressed by formula (7)Relationship between amplitude of fading α, then according to Jacobi Determinant, which converts to obtain, receives symbol signal-to-noise ratioProbability density functionAre as follows:
Consider binary system BPSK digital modulation, the bit error rate P under coherent demodulationb(γ) expression formula are as follows:
The average error rate of BPSK under MRC merging modeAre as follows:
Wherein,
Step 5: being by receiving that maximum branch of symbol signal-to-noise ratio in L tributary signal of selection using SC merging Road is as output, and in each branch weighting coefficient of formula (1), the coefficient of only one branch is not zero, and remaining branch Coefficient is zero, that is, ai=1, aj=0, i ≠ j, i, j ∈ [1,2 ..., L];SC exports prompt character signal-to-noise ratioAre as follows:
Wherein,Subscript SC indicate selection combining, subscript s indicate symbol signal-to-noise ratio;If between all merging branches It declines irrelevant, then the cumulative distribution function of prompt character signal-to-noise ratioAre as follows:
Wherein, γ is given signal-to-noise ratio numerical value, can obtain the wink under SC merging mode by carrying out differential to formula (12) When receive symbol signal-to-noise ratio probability density functionAre as follows:
According to formula (9), using the average error rate of BPSK modulation under SC merging mode are as follows:
WhenAt this point, right?Place carries out the approximate table that Taylor expansion obtains formula (14) Up to formula are as follows:
Wherein,It isN order derivative is asked to exist laterThe value at place, whenWhen, obtain formula (10) approximate expression is:
According to formula (15) formula and formula (16), obtain:
When can thus obtain using L branch MRC merging, the approximate expression of the average error rate of bpsk signal is
As a kind of method side of advanced optimizing of assessment BPSK high specific reception merging error performance of the present invention Case, L=2.
As a kind of method side of advanced optimizing of assessment BPSK high specific reception merging error performance of the present invention Case, L=3.
As a kind of method side of advanced optimizing of assessment BPSK high specific reception merging error performance of the present invention Case, L=4.
The invention adopts the above technical scheme compared with prior art, has following technical effect that the present invention considers AWGN Under Rayleigh fading environment, when communication system uses BPSK digital modulation and coherent demodulation, tool L branch MRC diversity merges The approximation of receiver error performance simplifies appraisal procedure;The present invention is that BPSK letter under Rayleigh declines is obtained by mathematical derivation The complicated accurate closed-form expression of the bit error rate after the processing of MRC and SC folding number is respectively adopted, then according to high s/n ratio Under the conditions of SC merge error code expression formula Taylor expansion, obtain it is a kind of using the summation of series indicate simplify express, finally look for again MRC and SC these two types simplify in the corresponding connection of fixed direct proportion between relational expression, to obtain MRC under the conditions of to high s/n ratio Merge a kind of simplified acquiring method of error performance.
Detailed description of the invention
Fig. 1 is to receive diversity to merge the functional block diagram realized.
Fig. 2 is is proposed approximation method and MRC merging average error rate with the variation pair of average received signal-to-noise ratio using the present invention Than curve graph (by taking diversity branch number L=2 and L=3 as an example).
Specific embodiment
Technical solution of the present invention is described in further detail with reference to the accompanying drawing:
The embodiment of the present invention is by proposing that a kind of bpsk signal MRC receives the method for merging error performance assessment as such as It carries out the research of multi-channel diversity receiver performance and the analysis of the performance indicators such as system outage probability, error rate is mentioned For foundation.
About the multichannel receiver with L diversity branch, receives diversity Unite principle block diagram and set as shown in Figure 1: It is r that the band logical of the branch of receiving end L, which receives signal,1(t),r2(t),...,rL(t), wherein rk(t) for kth (k=1,2 ..., L) paths received signal copy.The bandpass signal that different antennae branch receives is through multicarrier orthogonal demodulation coherent detection The vector form that baseband signal is obtained after (matched filtering) isThe letter of output to the end is obtained using different diversity combiners again Number vectorFor L input signal of receiving end, finally merge signal output are as follows:
In above formula, akFor weighting coefficient, configured according to different weighting coefficients, available different merging mode.No Generality is lost, it can be to akIt is normalized:
Under Rayleigh fading channel, the amplitude of fading of system transmission symbol meets Rayleigh distribution, and probability is close Spend function (Probability Density Function, PDF) fα(α) are as follows:
Wherein, e is the nature truth of a matter, and σ is constant and 0,2 σ of σ >2=E [α2] be amplitude of fading α mean-square value, mean valueVariance D [α]=(4- π) σ2/2.In addition to Rayleigh decline factor, AWGN, power spectrum are also contained in channel Density is N0;Assuming that sending end signal emitted energy is Es, every branch receiving end signal instantaneous signal-to-noise ratio is denoted as γk, institute it is right The average received signal-to-noise ratio answered is denoted asThen have:
According to the instantaneous signal-to-noise ratio γ for every branch receiving end signal that above formula obtainskWith the relationship of amplitude of fading α, then according to Instantaneous received signal to noise ratio γ can be calculated according to Jacobian transformationkPDF are as follows:
When being merged using MRC, receiver is according to the weighting coefficient in certain rule adjustment (1) formula and through same phase processor Afterwards, the signal-to-noise ratio for finally merging obtained output signal with order is maximum, at this time its each branch weighting coefficient akWith tributary signal packet Network is proportional, inversely with noise power, may be expressed as: akk/Nk, wherein αkIndicate the packet of kth branch Network, NkIndicate noise power.Assuming that each branch mutually balances, i.e., at the radio frequencies such as consistent, power amplifier of ambient noise of every branch road When the external environments such as reason device and scattering are consistent, then under Rayleigh fading channel, envelope αkRayleigh distribution is obeyed, And αk 2Obey chi square distribution and E [αk 2The σ of]=22, then in square of the total envelope in receiving endIt is to obey freedom degree as 2L Chi square distribution and its PDF are as follows:
Wherein, Γ () is Gamma function, has Γ (L)=(L-1) when L is positive integer!.Each symbol of receiving end Corresponding average received signal-to-noise ratioWith output prompt character signal-to-noise ratioValue be respectively:
In above formula,Subscript MRC indicate that maximum-ratio combing, subscript s indicate symbol, therefore it is entireRepresent MRC conjunction Instantaneous reception symbol signal-to-noise ratio under the conditions of and.According to expressed by above formulaRelationship between amplitude of fading α, then according to refined Gram than determinant transformation can must receive symbol signal-to-noise ratioPDFAre as follows:
Consider binary system BPSK digital modulation, the theoretical bit error rate P under coherent demodulationb(γ) expression formula are as follows:
By the derivation of a series of complex, can obtain the average error rate of BPSK under MRC merging mode is
In above formula,
Expression formula by above-mentioned formula (10) in relation to bpsk signal theoretical bit error rate under MRC merging is it is recognized that while can be with Obtain the closure expression under the conditions of MRC, but the calculating of the expression formula be related to multinomial combinatorial operation, exponent arithmetic and they multiply The accumulating operation of product item sum, thus be not it is very convenient, especially in mobile terminal using the hardware resources such as DSP or FPGA Come when carrying out system performance judgement, it will increase hardware resource cost and be unfavorable for the demands of green communications.Exactly for this Consider, below we just propose it is a kind of bit error analyzing is merged based on SC, what related MRC merged error performance assessment simplifies approximation Method.
So-called SC merging is by selecting to receive that maximum branch of symbol signal-to-noise ratio in L tributary signal as defeated Reception technique out, i.e., in each branch weighting coefficient of (1) formula, the coefficient of only one branch is not zero, and remaining branch Coefficient be zero, that is, ai=1, aj=0 (i ≠ j), (i, j ∈ [1,2 ..., L]).SC exports prompt character signal-to-noise ratioAre as follows:
In above formula,Subscript SC indicate selection combining, subscript s indicate symbol signal-to-noise ratio.If all merging branches it Between decline it is irrelevant, then cumulative distribution function (the Cumulative Distribution of prompt character signal-to-noise ratio Function, CDF)Are as follows:
Wherein, γ is given signal-to-noise ratio numerical value.It can be obtained under SC merging mode by carrying out differential to above-mentioned formula (12) Instantaneous reception symbol signal-to-noise ratio PDFAre as follows:
It uses for reference formula (9), through deriving, using the average error rate of BPSK modulation under SC merging mode are as follows:
It notices and works asAt this point, right?Place carries out Taylor expansion and obtains formula (14) Approximate expression are as follows:
In above-mentioned formula (15),It isN order derivative is asked to exist laterThe value at place.Equally, whenWhen, also the approximate expression of available formula (10) is:
It is seen that (15) formula and (16) formula have therebetween following relationship
When can thus obtain bpsk signal using L branch MRC merging, the approximate expression of average error rate is
, it is apparent that being compared to MRC merges accurately calculating for the lower BPSK theory bit error rate from above-mentioned (18) formula Formula (10) is compared, gained bpsk signal using L branch MRC merge when average error rate approximate expression (18) do not need into The operations such as row Polynomial combination, power series product and summation, difficulty in computation and complexity are decreased obviously.The present invention is according to above-mentioned Formula (18) solves the problems, such as that the computation complexity of the BPSK theory bit error rate under MRC merges is high, can be applied to rapid evaluation The bit error rate performance of mimo system, one of advantage are a simplified computation complexity, advantage second is that can be to error rate of system Performance is accurately estimated.
Fig. 2 gives when making emulation example with diversity branch number L=2 and L=3, is mentioned using the present invention based on L branch SC conjunction And when approximate weight computation method and L branch MRC merging, bpsk signal receiving end average error rate performance is with average received noise Than changing contrast curve chart.It can be seen that the approximate weighting for proposing and merging based on SC from two groups of simulation curve results shown in the figure The average error rate curve of algorithm, which merges average error rate exact value curve with MRC, to be had with the consistent change of average received signal-to-noise ratio Change trend, and the error between them is very small.
Independence is respectively branched into multi-channel diversity receiver it can be seen from the specific implementation process that the above present invention provides Under Rayleigh fading profiles with distribution, merges the accurate error performance of BPSK coherent demodulation for complicated L branch MRC and comment Estimate, completely can with it is a kind of merge approximate derivation based on SC and carry out the simple calculation formula of fixed weighting replaced, from And reduce hardware resource cost of the receiver for System Performance Analysis.

Claims (5)

1. a kind of assessment BPSK high specific receives the method for merging error performance, which is characterized in that consider AWGN and Rayleigh Under fading environment, communication system uses BPSK digital modulation and coherent demodulation, and receiving end obtains the mutually independent branch letter of L item Number, the average error rate model of bpsk signal when L branch MRC merges is established, BPSK maximum is assessed according to average error rate Merge error performance than receiving;Wherein,
Average error rate model are as follows:
Wherein, L is the number of receiving end branch,For the corresponding average received signal-to-noise ratio of each symbol of receiving end.
2. a kind of assessment BPSK high specific according to claim 1 receives the method for merging error performance, which is characterized in that Specific step is as follows for the average error rate model for establishing bpsk signal when L branch MRC merges:
Step 1: the band logical for setting the branch of receiving end L receives signal as r1(t),r2(t),...,rL(t), different antennae branch connects The vector form that the bandpass signal received obtains baseband signal after multicarrier orthogonal demodulation matched filtering isAgain using difference Diversity combiner obtain output signal vector to the endWherein, rkIt (t) is kth paths received signal copy, k=1, 2,...,L;
Step 2: finally merging signal output for L input signal of receiving end are as follows:
Wherein, akFor weighting coefficient;
To akIt is normalized:
Step 3: the amplitude of fading α of system transmission symbol meets Rayleigh distribution, general under Rayleigh fading channel Rate density function fα(α) are as follows:
Wherein, e is the nature truth of a matter, and σ is constant and 0,2 σ of σ >2=E [α2] be amplitude of fading α mean-square value, mean valueVariance D [α]=(4- π) σ2/2;The power spectral density of additive white Gaussian noise AWGN is N in channel0;If Transmission end signal emitted energy is Es, every branch receiving end signal instantaneous signal-to-noise ratio is denoted as γk, corresponding to average received Signal-to-noise ratio is denoted asThen have:
According to the instantaneous signal-to-noise ratio γ for every branch receiving end signal that formula (4) obtainskWith the relationship of amplitude of fading α, then foundation Jacobian transformation calculations go out instantaneous received signal to noise ratio γkProbability density functionAre as follows:
Step 4: when being merged using MRC, akk/Nk, wherein αkIndicate the envelope of kth branch, NkIndicate noise power;If Each branch mutually balances, under Rayleigh fading channel, envelope αkRayleigh is obeyed to be distributed, and αk 2Obey chi square distribution and E[αk 2The σ of]=22, then in square of the total envelope in receiving endIt is to obey the chi square distribution and its probability that freedom degree is 2L Density function fα(α) are as follows:
Wherein, Γ () is Gamma function, has Γ (L)=(L-1) when L is positive integer!;Each symbol of receiving end is corresponding Average received signal-to-noise ratioWith output prompt character signal-to-noise ratioValue be respectively:
Wherein,Subscript MRC indicate maximum-ratio combing, subscript s indicate symbol,Represent the wink under the conditions of MRC merges When receive symbol signal-to-noise ratio;According to expressed by formula (7)Relationship between amplitude of fading α, then according to Jacobi ranks Formula, which converts to obtain, receives symbol signal-to-noise ratioProbability density functionAre as follows:
Consider binary system BPSK digital modulation, the bit error rate P under coherent demodulationb(γ) expression formula are as follows:
The average error rate of BPSK under MRC merging modeAre as follows:
Wherein,
Step 5: using SC merging being made by receiving that maximum branch of symbol signal-to-noise ratio in L tributary signal of selection For output, in each branch weighting coefficient of formula (1), the coefficient of only one branch is not zero, and the coefficient of remaining branch It is zero, that is, ai=1, aj=0, i ≠ j, i, j ∈ [1,2 ..., L];SC exports prompt character signal-to-noise ratioAre as follows:
Wherein,Subscript SC indicate selection combining, subscript s indicate symbol;If the mutual not phase of all declines merged between branches It closes, then the cumulative distribution function of prompt character signal-to-noise ratioAre as follows:
Wherein, γ is given signal-to-noise ratio numerical value, can obtain instantaneously connecing under SC merging mode by carrying out differential to formula (12) Receive the probability density function of symbol signal-to-noise ratioAre as follows:
According to formula (9), using the average error rate of BPSK modulation under SC merging mode are as follows:
WhenAt this point, right?Place carries out the approximate expression that Taylor expansion obtains formula (14) Are as follows:
Wherein,It isN order derivative is asked to exist laterThe value at place, whenWhen, obtain formula (10) Approximate expression is:
According to formula (15) formula and formula (16), obtain:
When can thus obtain using L branch MRC merging, the approximate expression of the average error rate of bpsk signal is
3. a kind of assessment BPSK high specific according to claim 1 receives the method for merging error performance, which is characterized in that L=2.
4. a kind of assessment BPSK high specific according to claim 1 receives the method for merging error performance, which is characterized in that L=3.
5. a kind of assessment BPSK high specific according to claim 1 receives the method for merging error performance, which is characterized in that L=4.
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